The GCSE maths curriculum is huge, and it’s split by tier, so immediately there is an understanding that some students won’t be able to access it all by the end of year 11, but that does leave us as teachers with a dilemma. How much do we actually cover with our students.
In particular, if you have a group of students who are realistically only going to get a grade 1/2 on foundation, or 5/6 on higher, do you aim to cover all of the content with them, including the stuff they are really unlikely to grasp? If you do want to, how much depth can you actually achieve with them, especially on those more challenging topics. If you don’t want to cover it all, what gets left behind?
The reality is at the outset of their secondary journey you have three choices:
- Cover everything in depth.
- Cover everything, but for some topics you will only skim the surface.
- Don’t teach it all.
Let’s break them down:
Everything in depth
For most people this would be the ideal, cover all the curriculum fully and in depth so that all students get it, and can think and act mathematically even in the face of tricky exam questions.
The problem is it would require huge flexibility in the amount of time we have to spend with students. Some need far more time to develop their understanding than others. That isn’t possible when you’re trying to mass educate every child in the country with class sizes of 30, staff shortages, and an overloaded curriculum in most subjects.
We simply don’t have the hours necessary to get all students to learn all the maths by the time they are 16, and also have time to cover the curriculum in all of their other subjects.
Skim the surface
This does sound better right? Students still get that full curriculum experience, they still have a chance at answering all the exam questions, and if they find one topic tricky they might pick marks up elsewhere so it’s not such a bit deal.
The reality is this does sort of work with many students, particularly as you near exams in year 11, because you can teach them some vaguely memorable tricks to help them solve problems. Maths is crammed full of handy mnemonics for students to recite when faced with standard maths questions.
The downside now is that those students often haven’t got the faintest idea what they’re actually doing, so if you ask them anything non-standard they will be hopelessly lost. You might have the time to do this, but that time is being spent racing through material which is swiftly forgotten because there was no depth.
To really understand maths you need to build on your prior understanding, make connections with other ideas, grasp the structure of the problems you are tackling rather that just the surface number crunching. Those helpful memory tricks are more likely to be mis-remembered than useful if there is no deeper understanding to pin them to.
Sure, it might mean they sit in an exam and there is nothing “unfamiliar”, but that isn’t the same as being able to answer the questions.
Don’t cover it all
The third approach is to deliberately not teach everything. To teachers in other subjects this probably sounds like blasphemy. How could you even think of sending students into an exam knowing that they won’t have a clue how to even start on some of the questions?
This path is generally taken by staff who know (or at least think they know) in advance that certain topics will be inaccessible to their class, so time is better spent elsewhere securing the foundations. There are some clear pitfalls to this approach.
If you’ve never taught a topic, students have an immediate ceiling on their potential in an exam. If (when) those topics show up on the paper, they have no choice but to skip them (or guess, but that’s not likely to bear any fruit). And how do you choose what to skip? How do you know this class won’t cope with that idea? What if you skip the topic that your class would have absolutely nailed in a couple of lessons?
Deliberately avoiding topics in the curriculum is a complex business, but it does adequately solve the time problem. You just teach what you have the time to cover properly and don’t worry about the rest.
In conclusion
Do I have a preference? Well of course I do, but I’ll save that for the next post…